solve:
x lnx - 30 + 5 lnx - 6x = 0
duplicate post. already answered
My previous response (which I can't find) was that there is no solution to that equation
To solve the equation x ln(x) - 30 + 5 ln(x) - 6x = 0, we can follow the steps below:
Step 1: Combine like terms
Rearrange the terms in the equation:
x ln(x) + 5 ln(x) - 6x - 30 = 0
Step 2: Combine the logarithms
Combine the terms with the natural logarithm:
(x + 5) ln(x) - 6x - 30 = 0
Step 3: Factor out the common factor
Factor out (x + 5) from the first two terms:
(x + 5)(ln(x)) - 6x - 30 = 0
Step 4: Solve for the value of x
Setting each factor separately to zero:
x + 5 = 0 or ln(x) - 6 = 0
For x + 5 = 0, subtract 5 from both sides:
x = -5
For ln(x) - 6 = 0, add 6 to both sides:
ln(x) = 6
To eliminate the natural logarithm, exponentiate both sides using e as the base:
e^(ln(x)) = e^6
This simplifies to:
x = e^6
So, the solutions to the equation are: x = -5 and x = e^6.